[Paper Review] Conductance-based dendrites perform Bayes-optimal cue integration

Jakob Jordan, João Sacramento+3 more|arXiv (Cornell University)|Apr 27, 2021

Neural dynamics and brain function1 citations

TL;DR

This paper proposes that conductance-based dendrites in cortical pyramidal neurons implement Bayes-optimal cue integration by encoding prior expectations (apical dendrites) and likelihoods (basal dendrites) through local reversal potentials and conductances. The somatic membrane potential naturally computes the posterior via divisive normalization, and a gradient-based plasticity rule enables learning of reliable input weights, explaining multisensory integration and generating testable predictions on dendritic computation and synaptic plasticity.

ABSTRACT

A fundamental function of cortical circuits is the integration of information from different sources to form a reliable basis for behavior. While animals behave as if they optimally integrate information according to Bayesian probability theory, the implementation of the required computations in the biological substrate remains unclear. We propose a novel, Bayesian view on the dynamics of conductance-based neurons and synapses which suggests that they are naturally equipped to optimally perform information integration. In our approach apical dendrites represent prior expectations over somatic potentials, while basal dendrites represent likelihoods of somatic potentials. These are parametrized by local quantities, the effective reversal potentials and membrane conductances. We formally demonstrate that under these assumptions the somatic compartment naturally computes the corresponding posterior. We derive a gradient-based plasticity rule, allowing neurons to learn desired target distributions and weight synaptic inputs by their relative reliabilities. Our theory explains various experimental findings on the system and single-cell level related to multi-sensory integration, which we illustrate with simulations. Furthermore, we make experimentally testable predictions on Bayesian dendritic integration and synaptic plasticity.

Motivation & Objective

• To explain how cortical neurons perform Bayes-optimal integration of uncertain sensory cues using biologically plausible dendritic mechanisms.
• To demonstrate that conductance-based synaptic dynamics naturally implement Bayesian inference through divisive normalization.
• To develop a plasticity rule that allows neurons to learn target posterior distributions by adjusting synaptic weights according to input reliability.
• To unify single-neuron computation with system-level Bayesian behavior, explaining experimental findings in multisensory integration.
• To generate experimentally testable predictions on dendritic integration and synaptic weight adaptation.

Proposed method

• Models apical dendrites as encoding prior distributions over somatic potentials via effective reversal potentials and conductances.
• Models basal dendrites as encoding likelihoods of somatic potentials through similar conductance-based parameters.
• Uses leaky integrate-and-fire dynamics with conductance-based synapses to compute the posterior via divisive normalization.
• Derives a stochastic gradient ascent rule on the log-posterior to update synaptic weights based on target somatic activity and variance.
• Employs a two-compartment neuronal model with plastic synapses to simulate multisensory integration tasks.
• Validates the model through simulations of cue integration tasks with varying cue reliabilities and training protocols.

Experimental results

Research questions

• RQ1 Can conductance-based dendritic compartments naturally compute Bayesian posteriors through local membrane dynamics?
• RQ2 How do apical and basal dendrites collectively implement prior and likelihood encoding in a biologically plausible manner?
• RQ3 Can a single-neuron plasticity rule learn to weight inputs by their reliability to match target posterior distributions?
• RQ4 Does the proposed model reproduce behavioral and neural data from multisensory integration experiments?
• RQ5 What experimentally testable predictions does the theory generate regarding dendritic integration and synaptic plasticity?

Key findings

• Conductance-based dendrites compute the posterior distribution via divisive normalization of compartmental membrane potentials, enabling Bayes-optimal integration.
• The model successfully learns to weight inputs by their reliability, with less reliable inputs contributing less total excitatory and inhibitory conductance.
• Simulations demonstrate accurate classification in a multisensory cue integration task, with performance matching Bayes-optimal benchmarks.
• The trained model explains experimental data on cue integration, including the influence of prior expectations and modality-specific reliability.
• The theory predicts that synaptic plasticity adjusts weights based on both target activity and target variance, enabling dynamic reliability-based weighting.
• The framework provides a unified explanation for single-cell dynamics and system-level Bayesian behavior in cortical circuits.